Method for determining minimum sample number of profile line strip of three-dimensional roughness evaluation of structural plane

Abstract

A profile line strip minimum sample number determination method for evaluating three-dimensional roughness of a structural surface, comprising the following steps: S1, determining a measurement direction of three-dimensional roughness and an optimal width of a profile line strip; S2, measuring the profile line strip on the surface of the structural surface; S3, establishing a triangulation model of the profile line strip; S4, calculating the mean value and standard deviation of basic indexes of three-dimensional roughness of the structural surface; S5, according to the measurement error of three-dimensional roughness of the structural surface allowed by the project, inversely calculating the required minimum sample number of the profile line strip; S6, repeating steps S4 and S5 until the number of the measured profile line strip meets the requirement of the required minimum sample number of the profile line strip, and the number of the finally measured profile line strip is the minimum sample number of the profile line strip. The method solves the problems that the dimensional difference between a two-dimensional profile line and a three-dimensional structural surface morphology cannot be eliminated, the sampling interval is difficult to accurately determine, and the measurement sample number has no quantitative index.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for determining the minimum sample number of profile lines for evaluating the three-dimensional roughness of structural surfaces. Background Technology

[0002] Structural surface roughness has a significant impact on the mechanical and hydraulic properties of rock masses and is a key parameter in rock mass stability analysis. It is typically characterized by joint roughness coefficient (JRC), fractal dimension, and statistical parameters. In engineering practice, these roughness parameters can be conveniently estimated using two-dimensional profiles. However, the surface morphology of structural surfaces has three-dimensional characteristics. Given the dimensional difference between two-dimensional and three-dimensional roughness, whether using a single or multiple two-dimensional profiles can characterize the three-dimensional roughness of structural surfaces remains controversial.

[0003] When using two-dimensional profiles to evaluate the roughness of structural surfaces, some geometric features located within the profile intervals may be overlooked. Therefore, researchers have attempted to improve the accuracy of roughness evaluation by reducing the sampling interval of the profiles. Previous studies have typically used sampling intervals ranging from 0.1 mm to 15 mm to measure the profiles. Although existing studies have verified the impact of the profile sampling interval on roughness evaluation results, inconsistent results remain regarding the optimal sampling interval. For example, Bao et al. found that when the profile sampling interval is less than 4 mm, the average roughness of the profile remains unchanged regardless of the surface roughness. However, Ge et al. found that both the size and roughness of the surface significantly affect the optimal sampling interval of the profile. Therefore, the optimal sampling interval for two-dimensional profiles requires further exploration.

[0004] While reducing the sampling interval of two-dimensional profiles can improve the accuracy of structural surface roughness evaluation, measuring too many profiles is time-consuming and labor-intensive, which is not conducive to engineering practice. Therefore, determining the minimum number of profiles (RMN) required to obtain sufficiently accurate structural surface roughness is of great significance. Yong et al. conducted a graded analysis of 100cm long slate structural surface profiles and found that at least 65 profiles are needed to accurately evaluate the roughness of the structural surface. Bao et al. studied the geometric non-uniformity of structural surface roughness and suggested that the sampling interval of structural surface profiles should be less than 4mm. Existing research has provided inspiration for determining the RMN of profiles; however, the above work was conducted under certain conditions. Under these conditions, a large number of structural surface roughness measurements have been performed, and the statistical information of structural surface roughness is known. Evaluating the RMN of profiles by analyzing existing databases can provide a reference for structural surfaces with similar roughness. However, the research of Du Shigui et al. shows that structural surface roughness is non-uniform and varies significantly in different locations. In most cases, reliable prior statistical information about structural surface roughness cannot be obtained. In fact, statistical information about the surface roughness of a structure can only be gradually revealed during the roughness measurement process. Therefore, it is necessary to dynamically determine whether the measured profile is sufficient to reliably evaluate the surface roughness during the measurement process.

[0005] Given the variability of two-dimensional profile roughness, researchers and engineers typically use the average roughness of the profile as a representative roughness value for the structured surface. To investigate the effectiveness of profiles in characterizing the three-dimensional roughness of structured surfaces, researchers have conducted extensive work comparing the differences between two-dimensional and three-dimensional roughness. For example, Belem et al. found that the rougher the structured surface, the more the average two-dimensional roughness underestimates the three-dimensional roughness. However, Tatone and Grasselli found that the average two-dimensional roughness can either overestimate or underestimate the three-dimensional roughness. These findings suggest that the average roughness of the profile may not be an effective measure of the three-dimensional roughness of the structured surface. Therefore, some researchers have proposed other methods for processing two-dimensional roughness to evaluate the three-dimensional roughness of structured surfaces. For example, Liu et al. used the maximum two-dimensional roughness of the profile to analyze their experimental results, while Huan Jiuyang used the weighted average two-dimensional roughness of the profile to evaluate the three-dimensional roughness of the structured surface. These processing methods for two-dimensional roughness of the profile (i.e., average roughness, maximum roughness, and weighted average roughness) have promoted the application of profiles in evaluating the three-dimensional roughness of structured surfaces. However, inconsistent results from different processing methods diminish the practicality of profile lines. This inconsistency may be because the dimensional differences between two-dimensional profile lines and three-dimensional structural surface morphology cannot be eliminated simply by increasing the number of profile lines. Therefore, further research is needed on how to effectively utilize profile lines to evaluate the three-dimensional roughness of structural surfaces.

[0006] Two-dimensional profiles of structural surfaces are widely used in engineering practice for evaluating surface roughness due to their ease of acquisition and measurement. While profiles have been successfully applied to evaluate two-dimensional surface roughness, their application in evaluating three-dimensional roughness still faces challenges, including difficulty in accurately determining the sampling interval, lack of quantitative indicators for the number of measurements, and the inability to eliminate dimensional differences between two-dimensional profiles and three-dimensional structural surface morphology. Therefore, the reliability of evaluation results using two-dimensional profiles for evaluating three-dimensional surface roughness is insufficient, directly affecting the accuracy of the evaluation results for the mechanical and hydraulic properties of the structural surface. Summary of the Invention

[0007] To overcome the problems of existing technologies that use two-dimensional profile lines to evaluate the three-dimensional roughness of structural surfaces, such as the inability to eliminate the dimensional differences between the two-dimensional profile lines and the three-dimensional structural surface morphology, the difficulty in accurately determining the sampling interval, and the lack of quantitative indicators for the number of measurements, this invention provides a method for determining the minimum sample number of profile line bands for evaluating the three-dimensional roughness of structural surfaces. This method uses profile line bands composed of adjacent profile lines instead of a single profile line to characterize the three-dimensional local morphology of the structural surface. It proposes the optimal width of the profile line bands for structural surfaces of different sizes and dynamically determines whether the number of samples of the measured profile line bands is sufficient to reliably evaluate the three-dimensional roughness of the structural surface during the measurement process. This provides a quantitative indicator for the minimum sample number of profile line bands required for evaluating the three-dimensional roughness of structural surfaces, which can effectively promote the engineering application of two-dimensional profile lines in the evaluation of the three-dimensional roughness of structural surfaces.

[0008] The technical solution adopted by this invention to solve its technical problem is:

[0009] A method for determining the minimum sample number of profile lines for three-dimensional roughness evaluation of structural surfaces, the method comprising the following steps:

[0010] S1. Select the structural surface outcrop, determine the measurement direction of the three-dimensional roughness and the optimal width of the profile line band; the profile line band is composed of two adjacent profile lines, and its width is equal to the distance between the two adjacent profile lines.

[0011] S2. Based on the measurement direction and the optimal width of the profile line band, measure the profile line band on the surface of the structure.

[0012] S3. Use a high-precision scanner and image processing technology to digitize the measured profile line bands and establish a triangulated model of the profile line bands.

[0013] S4. Based on the established triangulation model of the profile lines, calculate the mean and standard deviation of the basic three-dimensional roughness index of the structural surface.

[0014] S5. Based on the allowable three-dimensional roughness measurement error of the structural surface in the project, calculate the minimum number of samples required for the cross-sectional line band according to the following formula (1);

[0015]

[0016] Where δ represents the measurement error of the three-dimensional roughness of the structural surface, s represents the standard deviation of the basic three-dimensional roughness index of the profile strip, μ represents the mean of the basic three-dimensional roughness index of the profile strip, n represents the number of profile strip measurements, and β represents the confidence level. Let be the upper quantile of the t-distribution with n-1 degrees of freedom;

[0017] S6. Repeat steps S4 and S5 during the measurement of the profile line bands until the number of measured profile line bands meets the requirement of the minimum sample number of the required profile line bands calculated by back calculation. The final number of measured profile line bands is the minimum sample number of the profile line bands.

[0018] Furthermore, in step S1, the measurement direction of the three-dimensional roughness is consistent with the shear direction of the structural surface or the seepage direction of the crack; when the structural surface size is less than or equal to 300 mm, the optimal width of the cross-sectional line band is 3 mm; when the structural surface size is greater than 300 mm, the optimal width of the cross-sectional line band is 5 mm.

[0019] Furthermore, in step S3, when performing triangulation modeling on the cross-sectional line band, the sampling point spacing used is consistent with the sampling point spacing in the calculation formula of the basic index of three-dimensional roughness of the structural surface.

[0020] Furthermore, in step S4, the basic index of three-dimensional roughness is the three-dimensional average tilt angle θ of the structural surface. s Root mean square Z of the three-dimensional slope of the structural surface 2s and the structural surface area projection ratio R s The calculation formula is as follows:

[0021]

[0022]

[0023]

[0024] Among them, M x M y Let α be the number of sampling points uniformly distributed along the X and Y axes, respectively. i Let A be the angle of inclination of the outward normal vector of the i-th triangle element, i.e., the angle between the outward normal vector of the triangle plane and the Z-axis. t A is the actual area of ​​the structural surface. n Let a be the projected area of ​​the structural surface on the XY plane. i Let SI be the area of ​​the i-th triangle element, and let SI be the sampling interval of the point cloud.

[0025] Compared with existing technologies, the beneficial effects of this invention are mainly reflected in the following aspects: Using a cross-sectional line band composed of adjacent cross-sectional lines instead of a single cross-sectional line to characterize the three-dimensional local morphology of the structural surface can effectively eliminate the dimensional difference between the two-dimensional cross-sectional line and the three-dimensional morphology of the structural surface; employing different optimal widths of cross-sectional line bands for structural surfaces of different sizes can significantly reduce measurement time while ensuring the accuracy of three-dimensional roughness measurement; dynamically judging whether the number of measured cross-sectional line band samples meets the requirement of the minimum number of cross-sectional line band samples calculated in reverse during the measurement process can provide a quantitative indicator for the minimum number of cross-sectional line band samples required for three-dimensional roughness evaluation of structural surfaces, accurately evaluating the three-dimensional roughness of structural surfaces while avoiding resource waste, and effectively promoting the engineering application of two-dimensional cross-sectional lines in the evaluation of three-dimensional roughness of structural surfaces. Attached Figure Description

[0026] Figure 1 These are the local triangular units and profile lines extracted from the structural surface triangulation model, where (a) is the structural surface triangulation model, (b) is the local triangular unit, and (c) is the profile line.

[0027] Figure 2 The influence of the width of the profile line band on the three-dimensional roughness evaluation results;

[0028] Figure 3 It is a schematic diagram of the cross-sectional lines with measurements;

[0029] Figure 4 This indicates the location of the section line band. The image only shows one section line on the left side of the section line band, and the width of the section line band is 3mm. Detailed Implementation

[0030] The present invention will now be further described with reference to the accompanying drawings.

[0031] Reference Figures 1-4 A method for evaluating the three-dimensional roughness of structural surfaces based on profile lines, the method comprising the following steps:

[0032] S1. Select the structural surface outcrop, determine the measurement direction of the three-dimensional roughness and the optimal width of the profile line band; the profile line band is composed of two adjacent profile lines, and its width is equal to the distance between the two adjacent profile lines.

[0033] S2. Based on the measurement direction and the optimal width of the profile line band, measure the profile line band on the surface of the structure.

[0034] S3. Use a high-precision scanner and image processing technology to digitize the measured profile line bands and establish a triangulated model of the profile line bands.

[0035] Specifically, the surface morphology of structural surfaces is typically constructed on the measured point cloud using triangulation methods. The Delaunay triangulation algorithm can be used to triangulate the measured profile lines. Through triangulation, the surface morphology of the structural surfaces can be discretized into a finite number of triangles, such as... Figure 1 As shown in (a); this method is widely used to characterize the geometric features of structured surfaces and has significant advantages in evaluating the three-dimensional roughness of structured surfaces; when evaluating the three-dimensional roughness of structured surfaces, the geometric features of the structured surface can be conveniently characterized by the inclination angle and area of ​​the triangular elements on its triangular surface model; two local triangular elements extracted from the triangular model of the structured surface are shown in (a). Figure 1 As shown in (b), the figure illustrates that the geometric features of two local triangular units T1 and T2 are controlled by two adjacent two-dimensional profile lines P1 and P2; however, the dip direction of the profile lines is inconsistent with the dip direction of the triangular units, and therefore the dip angle of the profile lines is different from that of the triangular units. These observations confirm that a single profile line cannot accurately reflect the three-dimensional morphological features of the structural surface; in contrast, the local three-dimensional morphological features of the structural surface can be accurately characterized by the combined morphology of two adjacent two-dimensional profile lines, which is called a profile line band, such as... Figure 1 As shown in (c), the width of the profile line band is equal to the distance between its two adjacent two-dimensional profile lines. Generally, the three-dimensional morphology of the structure surface can be decomposed into a series of profile line bands, and the number of profile line bands depends on the width of the profile line bands. Therefore, the roughness of multiple profile line bands can potentially be used to approximate the three-dimensional roughness of the entire surface of the structure surface.

[0036] S4. Based on the established triangulation model of the profile lines, calculate the mean and standard deviation of the basic three-dimensional roughness index of the structural surface.

[0037] S5. Based on the allowable three-dimensional roughness measurement error of the structural surface in the project, calculate the minimum number of samples required for the cross-sectional line band according to the following formula (1);

[0038]

[0039] Where δ represents the measurement error of the three-dimensional roughness of the structural surface, s represents the standard deviation of the basic three-dimensional roughness index of the profile strip, μ represents the mean of the basic three-dimensional roughness index of the profile strip, n represents the number of profile strip measurements, and β represents the confidence level. Let be the upper quantile of the t-distribution with n-1 degrees of freedom;

[0040] Specifically, in engineering practice, the measurement error δ of the three-dimensional roughness of the structural surface can be set to 5%, the confidence level β can be set to 95%, and the upper quantile of the t-distribution with n-1 degrees of freedom can be used. The value can be obtained by looking up a table or by calculation based on the number of profile lines measured;

[0041] S6. Repeat steps S4 and S5 during the measurement of the profile line bands until the number of measured profile line bands meets the requirement of the minimum sample number of the required profile line bands calculated by back calculation. The final number of measured profile line bands is the minimum sample number of the profile line bands.

[0042] Preferably, in step S1, the measurement direction of the three-dimensional roughness is consistent with the shear direction of the structural surface or the seepage direction of the crack; when the structural surface size is less than or equal to 300 mm, the optimal width of the cross-sectional line is 3 mm; when the structural surface size is greater than 300 mm, the optimal width of the cross-sectional line is 5 mm.

[0043] Specifically, five profile strip widths (1mm, 2mm, 3mm, 4mm, and 5mm) were used to study the influence of profile strip width on the accuracy of three-dimensional roughness evaluation of the structural surface. Under the condition that the measurement error δ of the three-dimensional roughness of the structural surface was set to 5% and the confidence level β was set to 95%, 30 random sampling tests were conducted for each width of the profile strip. After the measurement, the measurement error of the three-dimensional roughness of the structural surface obtained under each profile strip width was calculated, such as... Figure 2 As shown in the figure, the average sampling rate of structural surfaces of different sizes decreases with the increase of the width of the profile line band, indicating that increasing the width of the profile line band can effectively reduce the measurement time. The figure also shows that the measurement error of the three-dimensional roughness of the structural surface decreases with the increase of the structural surface size, but increases with the increase of the width of the profile line band. When the structural surface size is greater than 300 mm, the basic three-dimensional roughness index, the three-dimensional average tilt angle θ of the structural surface... s Root mean square Z of the three-dimensional slope of the structural surface 2s and the structural surface area projection ratio R s The measurement error is less than 5% under all profile line width conditions; however, when the structural surface size is less than 300 mm, the basic three-dimensional roughness index Z... 2s The measurement error is greater than 5% when the width of the profile line band is 5mm; therefore, for structural surfaces with a size less than or equal to 300mm, a profile line band width of 3mm is recommended as the optimal width, and for structural surfaces with a size greater than 300mm, a profile line band width of 5mm is recommended as the optimal width.

[0044] Furthermore, in step S3, when performing triangulation modeling on the cross-sectional line band, the sampling point spacing used is consistent with the sampling point spacing in the calculation formula of the basic index of three-dimensional roughness of the structural surface.

[0045] Specifically, the point cloud data of the profile line band can be regularized so that the point cloud spacing of the established triangular profile line band model is consistent with the point spacing required by the calculation formula of the basic index of the three-dimensional roughness of the structural surface to be calculated.

[0046] Preferably, in step S4, the basic index of three-dimensional roughness is the three-dimensional average tilt angle θ of the structural surface. s Root mean square Z of the three-dimensional slope of the structural surface 2s and the structural surface area projection ratio R s The calculation formula is as follows:

[0047]

[0048]

[0049]

[0050] Among them, M x M y Let α be the number of sampling points uniformly distributed along the X and Y axes, respectively. i Let A be the angle of inclination of the outward normal vector of the i-th triangle element, i.e., the angle between the outward normal vector of the triangle plane and the Z-axis. t A is the actual area of ​​the structural surface. n Let a be the projected area of ​​the structural surface on the XY plane. i Let SI be the area of ​​the i-th triangle element, and let SI be the sampling interval of the point cloud.

[0051] Specifically, the basic index of three-dimensional roughness θ s Z 2s and R s These three-dimensional roughness indices can respectively reflect the average tilt angle characteristics, local tilt angle characteristics, and size characteristics of surface protrusions. The tilt degree and size of the protrusions on the surface of the structure are the basic roughness factors affecting the mechanical and hydraulic performance of the structure. Therefore, the selected three-dimensional roughness indices are sufficient to quantify the three-dimensional roughness of the structure. In addition, to further improve the evaluation accuracy of the three-dimensional roughness of the structure, more three-dimensional roughness parameters (such as undulation height parameters) can be included in the three-dimensional roughness indices.

[0052] Example: A method for evaluating the three-dimensional roughness of structural surfaces based on profile line bands, comprising the following steps:

[0053] First, a sandstone outcrop of a structural surface was selected in the Majiagou landslide area of ​​Guizhou Town, Zigui County, Yichang City, Hubei Province. The direction of the three-dimensional roughness measurement was consistent with the shear direction of the structural surface. The size of the structural surface was about 100 mm, so the optimal width of the profile line band was 3 mm.

[0054] Then, based on the measurement direction and the optimal width of the profile line band, a profile curve instrument is used to measure the profile line band on the surface of the structure. A high-precision scanner and image processing technology are used to digitize the measured profile line band. The Delaunay triangulation algorithm is used to triangulate the measured profile line band, and a triangulation model of the profile line band is established using a sampling interval of 0.5 mm. Figure 3 As shown; the three-dimensional average dip angle θ of the structural surface. s Root mean square Z of the three-dimensional slope of the structural surface 2s and the structural surface area projection ratio R s As a basic index of three-dimensional roughness, based on the established triangulation model of the profile line band, the mean and standard deviation of the basic index of three-dimensional roughness of the structural surface are calculated; the measurement error δ of the three-dimensional roughness of the structural surface is set to 5%, the confidence level β is set to 95%, and the minimum number of profile line bands required is calculated according to formula (1); during the measurement of the profile line band, steps S4 and S5 are repeated until the number of measured profile line bands meets the requirement of the minimum number of profile line bands required by the back calculation. Finally, the number of measured profile line bands is 9, and the positions of the profile line bands are as follows. Figure 4 As shown, the minimum number of profile lines required for this three-dimensional roughness evaluation of the structural surface is 9.

[0055] The root mean square Z-square of the three-dimensional slope of the structural surface is calculated based on the established triangulated model of the profile lines. 2s Then, the three-dimensional joint roughness coefficient JRC is calculated according to the formula (5) proposed by Mo and Li. The calculation result is 11.1. The true value of the three-dimensional JRC of the structure surface is 11.8 based on the direct shear test. The relative error between the three-dimensional roughness evaluation result of the structure surface based on the cross-sectional line band and the true value is only -5.9%, indicating that the present invention can conveniently and accurately evaluate the three-dimensional roughness of the structure surface.

[0056]

[0057] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for determining the minimum sample number of profile lines for three-dimensional roughness evaluation of structural surfaces, characterized in that, The method includes the following steps: S1. Select the structural surface outcrop, determine the measurement direction of the three-dimensional roughness and the optimal width of the profile line band; the profile line band is composed of two adjacent profile lines, and its width is equal to the distance between the two adjacent profile lines. S2. Based on the measurement direction and the optimal width of the profile line band, measure the profile line band on the surface of the structure. S3. Use a high-precision scanner and image processing technology to digitize the measured profile line bands and establish a triangulated model of the profile line bands. S4. Based on the established triangulation model of the profile lines, calculate the mean and standard deviation of the basic three-dimensional roughness index of the structural surface. S5. Based on the allowable three-dimensional roughness measurement error of the structural surface in the project, calculate the minimum number of samples required for the cross-sectional line band according to the following formula (1); Where δ represents the measurement error of the three-dimensional roughness of the structural surface, s represents the standard deviation of the basic three-dimensional roughness index of the profile strip, μ represents the mean of the basic three-dimensional roughness index of the profile strip, n represents the number of profile strip measurements, and β represents the confidence level. Let be the upper quantile of the t-distribution with n-1 degrees of freedom; S6. Repeat steps S4 and S5 during the measurement of the profile line bands until the number of measured profile line bands meets the requirement of the minimum sample number of the required profile line bands calculated by back calculation. The final number of measured profile line bands is the minimum sample number of the profile line bands.

2. The method for determining the minimum sample number of profile lines for three-dimensional roughness evaluation of structural surfaces as described in claim 1, characterized in that, In step S1, the measurement direction of the three-dimensional roughness is consistent with the shear direction of the structural surface or the seepage direction of the crack; when the structural surface size is less than or equal to 300 mm, the optimal width of the cross-sectional line is 3 mm; when the structural surface size is greater than 300 mm, the optimal width of the cross-sectional line is 5 mm.

3. The method for determining the minimum sample number of profile lines for three-dimensional roughness evaluation of structural surfaces as described in claim 1 or 2, characterized in that, In step S3, when performing triangulation modeling on the cross-sectional line band, the sampling point spacing used is consistent with the sampling point spacing in the calculation formula of the basic index of three-dimensional roughness of the structural surface.

4. The method for determining the minimum sample number of profile lines for three-dimensional roughness evaluation of structural surfaces as described in claim 1 or 2, characterized in that, In step S4, the basic index of three-dimensional roughness is the three-dimensional average tilt angle θ of the structural surface. s Root mean square Z of the three-dimensional slope of the structural surface 2s and the structural surface area projection ratio R s The calculation formula is as follows: Among them, M x M y Let α be the number of sampling points uniformly distributed along the X and Y axes, respectively. i Let A be the angle of inclination of the outward normal vector of the i-th triangle element, i.e., the angle between the outward normal vector of the triangle plane and the Z-axis. t A is the actual area of ​​the structural surface. n Let a be the projected area of ​​the structural surface on the XY plane. i Let SI be the area of ​​the i-th triangle element, and let SI be the sampling interval of the point cloud.

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